Gravitational waves from brane-world inflation with induced gravity

TL;DR

This paper calculates how induced gravity corrections affect the amplitude of gravitational waves and density perturbations during brane-world inflation, confirming the validity of the standard tensor/scalar ratio relation.

Contribution

It extends previous brane-world inflation models by including induced gravity effects and derives the corrected gravitational wave spectrum and consistency relation.

Findings

Zero-mode normalization depends on the brane Hubble rate

High energy corrections modify the gravitational wave spectrum

The tensor/scalar ratio consistency relation remains valid

Abstract

We calculate the amplitude of gravitational waves produced by inflation on a de Sitter brane embedded in five-dimensional anti-de Sitter bulk spacetime, extending previous calculations in Randall-Sundrum type cosmology to include the effect of induced gravity corrections on the brane. These corrections arise via a term in the brane action that is proportional to the brane Ricci scalar. We find that, as in the Randall-Sundrum case, there is a mass gap between the discrete zero-mode and a continuum of massive bulk modes, which are too heavy to be excited during inflation. We give the normalization of the zero-mode as a function of the Hubble rate on the brane and are thus able to calculate the high energy correction to the spectrum of gravitational wave (tensor) modes excited on large scales during inflation from initial vacuum fluctuations on small scales. We also calculate the amplitude of density (scalar) perturbations expected due to inflaton fluctuations on the brane, and show that the usual four-dimensional consistency relation for the tensor/scalar ratio remains valid for brane inflation with induced gravity corrections.